Electrons in Nanostructures: coherent manipulation and counting statistics

This thesis concerns theoretical aspects of electrons in man-made nanostruc- tures. Advances in nanofabrication technology during recent decades have made it possible to produce electrical devices on the nano-scale, whose func- tionality is determined by the quantum mechanical nature of a single or a few electrons. Such few-electron devices are expected to form the building blocks of future electrical circuits and it is thus necessary to develop a thorough theoretical understanding of the physics of electrons in nanostructures. Re- garding applications there is a particular interest in the possibilities o®ered by the quantum mechanical behavior of electrons when it comes to informa- tion processing. This branch of research is also concerned with fundamental questions in physics. Besides an introduction to the above-mentioned subjects, the thesis con- tains a number of contributions to the ¯elds of coherent electron manip- ulation and the statistical description of electron transport through nano- devices. The physics of the electrons are described with a combination of numerical methods, developed and applied in the thesis, and more analytical approaches, which are also discussed. The thesis contains a study of the in- teraction between the spins of electrons and proposals for novel methods of con¯ning and manipulating electrons in nanostructures. Moreover, a novel coupling mechanism between electron spins and light in the form of photons is described, which could ¯nd applications in quantum-based communication. The statistical description of electron transport through nanostructures is based on rate equations, and the primary contribution of the thesis in that respect is the development of a method that allows for the calculation of the distribution of electrons passing through a device. The method is illustrated with applications to two nano-electromechanical systems and is ¯nally ex- tended such that it also takes into account possible memory e®ects in the transport.